Abstract A general scheme for electrodynamics of composite multifilament superconductors is presented. Our approach is based on an anisotropic continuum model for a multifilament wire taking into account smooth dependence of superconductor conductivity on temperature, magnetic field and current density. The electrodynamics equations are self-consistently treated together with heat transfer. On the base of this scheme, 2D codes were developed for simulation of non-stationary processes in composite superconductors. A comparison of current density dynamics in twisted and non-twisted multifilament wires is presented as an example. The dynamics of current density in a twisted wire proved to be determined by two characteristic times and differs from the predictions based on the critical state model.